Issolvi ihbargamma^mupartial_{mu}psi=mcpsi

$$i \hbar \gamma ^ { \mu } \partial _ { \mu } \psi = m c \psi$$

Solvi għal c

$$\left\{\begin{matrix}c=\frac{iℏ∂_{μ}\gamma ^{\mu }}{m}\text{, }&m\neq 0\\c\in \mathrm{C}\text{, }&\psi =0\text{ or }\left(ℏ=0\text{ and }m=0\right)\text{ or }\left(\gamma =0\text{ and }\mu \neq 0\text{ and }m=0\right)\text{ or }\left(∂_{μ}=0\text{ and }m=0\right)\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$mc\psi =iℏ\gamma ^{\mu }∂_{μ}\psi$$

L-ekwazzjoni hija f'forma standard.

$$m\psi c=i\psi ℏ∂_{μ}\gamma ^{\mu }$$

Iddividi ż-żewġ naħat b'm\psi .

$$\frac{m\psi c}{m\psi }=\frac{i\psi ℏ∂_{μ}\gamma ^{\mu }}{m\psi }$$

Meta tiddividi b'm\psi titneħħa l-multiplikazzjoni b'm\psi .

$$c=\frac{i\psi ℏ∂_{μ}\gamma ^{\mu }}{m\psi }$$

Iddividi iℏ\gamma ^{\mu }∂_{μ}\psi b'm\psi .

$$c=\frac{iℏ∂_{μ}\gamma ^{\mu }}{m}$$

Solvi għal m

$$\left\{\begin{matrix}m=\frac{iℏ∂_{μ}\gamma ^{\mu }}{c}\text{, }&c\neq 0\\m\in \mathrm{C}\text{, }&\psi =0\text{ or }\left(ℏ=0\text{ and }c=0\right)\text{ or }\left(\gamma =0\text{ and }\mu \neq 0\text{ and }c=0\right)\text{ or }\left(∂_{μ}=0\text{ and }c=0\right)\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$mc\psi =iℏ\gamma ^{\mu }∂_{μ}\psi$$

L-ekwazzjoni hija f'forma standard.

$$c\psi m=i\psi ℏ∂_{μ}\gamma ^{\mu }$$

Iddividi ż-żewġ naħat b'c\psi .

$$\frac{c\psi m}{c\psi }=\frac{i\psi ℏ∂_{μ}\gamma ^{\mu }}{c\psi }$$

Meta tiddividi b'c\psi titneħħa l-multiplikazzjoni b'c\psi .

$$m=\frac{i\psi ℏ∂_{μ}\gamma ^{\mu }}{c\psi }$$

Iddividi iℏ\gamma ^{\mu }∂_{μ}\psi b'c\psi .

$$m=\frac{iℏ∂_{μ}\gamma ^{\mu }}{c}$$